'Official' answer:
The form which people fill in on the plane is actually a 'visa waiver' form which allows certain people to enter the USA without obtaining a visa. However, anyone who has ever been arrested or convicted of any offence is
not eligible for the visa waiver scheme and
must obtain a visa. (Minor motoring matters are exempted from the rules but this doesn't include drink-driving).
The visa application process is extremely lengthy. It takes
at least 5 months and, for much of this time, the applicant is effectively barred from leaving the UK. (This is because their passport will be held at the US embassy).
Details of the application process are in my post, here:
http://www.theanswerbank.co.uk/Travel/Question 289769.html
'Unofficial' answer:
The US authorities have no direct access to UK criminal records. While the UK authorities do pass some information on, this won't include drink-driving convictions. As long as you don't declare your conviction on the form, you should have no problem entering the USA. (If you do declare it, you risk being refused entry).
Chris